Abstract
In this manuscript, we consider a coupled AB system, which describes the baroclinic instability processes in the geophysical flows. Darboux-dressing transformation is used to derive the bright-dark soliton, breather and semirational rogue wave solutions for such a system. We observe that type of the solutions is relate to the spectral parameter \(\lambda \), amplitude \(a_{1}\) and wave number q. Elastic collision between dark or bright solitons, propagations of the bright or dark breathers and rogue waves coexist with two dark or bright solitons are respectively illustrated in figures. The results about those localized wave phenomena are expected to have potential applications.
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Wang, M., Chen, Y.: Dynamic behaviors of mixed localized solutions for the three-component coupled Fokas-Lenells system. Nonlinear Dynam. 98, 1781 (2019)
Meng, G.Q.: High-order semi-rational solutions for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling. Appl. Math. Lett. 105, 106343 (2020)
Wang, L., Liu, C., Wu, X., Wang, X., Sun, W.R.: Dynamics of superregular breathers in the quintic nonlinear Schrödinger equation. Nonlinear Dynam. 94, 977 (2018)
Xie, X.Y., Yang, S.K., Ai, C.H., Kong, L.C.: Integrable turbulence for a coupled nonlinear Schrödinger system. Phys. Lett. A 384, 126119 (2020)
Kong, L.Q., Wang, L., Wang, D.S., Dai, C.Q., Wen, X.Y., Xu, L.: Evolution of initial discontinuity for the defocusing complex modified KdV equation. Nonlinear Dynam. 98, 691 (2019)
Hasegawa, A., Tappert, F.: Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal Dispersion. Appl. Phys. Lett. 23, 171 (1973)
Mollenauer, L.F., Stolen, R.H., Gordon, J.P.: Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 45, 1095 (1980)
Zhang, G., Yan, Z.: The n-component nonlinear Schrödinger equations: dark-bright mixed N-and high-order solitons and breathers, and dynamics. P. Roy. Soc. A-Math. Phys. 474, 20170688 (2018)
Kivshar, Y.S., Flach, S.: Focus issue-Nonlinear localized modes: Physics and applications. Chaos 13, 586 (2003)
Baronio, F., Degasperis, A., Conforti, M., Wabnitz, S.: Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. Phys. Rev. Lett. 109, 044102 (2012)
Soto-Crespo, J.M., Devine, N., Akhmediev, N.: Integrable turbulence and rogue waves: breathers or solitons? Phys. Rev. Lett. 116, 103901 (2016)
Chabchoub, A., Hoffmann, N., Onorato, M., Akhmediev, N.: Super rogue waves: observation of a higher-order breather in water waves. Phys. Rev. X 2, 011015 (2012)
Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Optical rogue waves. Nature 450, 1054 (2007)
Moslem, W.M., Shukla, P.K., Eliasson, B.: Surface plasma rogue waves. EPL 96, 25002 (2011)
Bludov, Y.V., Konotop, V.V., Akhmediev, N.: Matter rogue waves. Phys. Rev. A 80, 033610 (2009)
Shats, M., Punzmann, H., Xia, H.: Capillary rogue waves. Phys. Rev. Lett. 104, 104503 (2010)
Peregrine, D.H.: Water waves, nonlinear Schrödinger equations and their solutions. J. Aust. Math. Soc. Ser. B 25, 16 (1983)
Ankiewicz, A., Soto-Crespo, J.M., Akhmediev, N.: Rogue waves and rational solutions of the Hirota equation. Phys. Rev. E 81, 046602 (2010)
Guan, X., Liu, W., Zhou, Q., Biswas, A.: Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation. Nonlinear Dynam. 98, 1491 (2019)
Liu, S., Zhou, Q., Biswas, A., Liu, W.: Phase-shift controlling of three solitons in dispersion-decreasing fibers. Nonlinear Dynam. 98, 395 (2019)
Baronio, F., Degasperis, A., Conforti, M., Wabnitz, S.: Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. Phys. Rev. Lett. 109, 044102 (2012)
Wu, C.F., Grimshaw, R.H.J., Chow, K.W., Chan, H.N.: A coupled AB system: Rogue waves and modulation instabilities. Chaos 25, 103113 (2015)
Xie, X.Y., Meng, G.Q.: Dark-soliton collisions for a coupled AB system in the geophysical fluids or nonlinear optics. Mod. Phys. Lett. B 32, 1850039 (2018)
Su, J.J., Gao, Y.T., Ding, C.C.: Darboux transformations and rogue wave solutions of a generalized AB system for the geophysical flows. Appl. Math. Lett. 88, 201 (2019)
Xie, X.Y., Meng, G.Q.: Multi-dark soliton solutions for a coupled AB system in the geophysical flows. Appl. Math. Lett. 92, 201 (2019)
Matveev, V.B., Salle, M.A.: Darboux Transformations and Solitons. Springer, Berlin (1991)
Degasperis, A., Lombardo, S.: Multicomponent integrable wave equations: II soliton solutions. J. Phys. A 42, 385206 (2009)
Stegeman, G.I., Segev, M.: Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518 (1999)
Xie, X.Y., Liu, X.B.: Elastic and inelastic collisions of the semirational solutions for the coupled Hirota equations in a birefringent fiber. Appl. Math. Lett. 105, 106291 (2020)
Frisquet, B., Kibler, B., Morin, P., Baronio, F., Conforti, M., Millot, G., Wabnitz, S.: Optical dark rogue wave. Sci. Rep. 6, 20785 (2016)
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This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11905061 and by the Fundamental Research Funds for the Central Universities (No. 2018MS132).
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Xie, XY., Liu, ZY. & Xu, DY. Bright-dark soliton, breather and semirational rogue wave solutions for a coupled AB system. Nonlinear Dyn 101, 633–638 (2020). https://doi.org/10.1007/s11071-020-05794-1
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DOI: https://doi.org/10.1007/s11071-020-05794-1